The universal two-fifths law of pier scour

Abstract

Understanding scour at bridge piers is crucial for safeguarding public safety, ensuring infrastructure resilience, and planning effective maintenance. Despite over six decades of extensive studies aiming to develop predictive formulas for the equilibrium scour depth at bridge piers, more than 20 000 highway bridges in the United States have been spotted “scour critical.” The traditional reliance on existing empirical formulas has posed a severe challenge for researchers, hindering to achieve a unified relation for the equilibrium scour depth from a fundamental scientific tenet. This perspective article presents a breakthrough—a universal law governing the equilibrium scour depth at a circular pier embedded in a sediment bed, specifically in clear-water scour condition. Derived from a phenomenological model, the universal law reveals that the equilibrium scour depth to pier diameter ratio obeys a consistent two-fifths scaling law with the introduction of a newly coined pier-scour number. This number accounts for all the key parameters involved in a local scour phenomenon, including the approach mean flow velocity, threshold shear velocity for sediment grain motion, approach flow depth, pier diameter, and sediment grain size. Importantly, the scaling law contains an additional term involving the drag coefficient raised to the power of 2/5, addressing the impact of the pier shape on the equilibrium scour depth. The derived universal law undergoes the validation through an extensive dataset of experimental measurements on circular pier scour.